Thus we see that the solution is already naturally in the Ellis-wormhole ansatz with the wormhole throat at \(r=0\)  and wormhole radius \(q\) . As \(r\)  runs from \(-\infty \)  to \(+\infty \) , the scalar runs from \(\phi _-=-\pi \)  to \(\phi _+=\pi \) , with \(V_\pm =\Lambda ^*\) . The solution describes a symmetric AdS wormhole, and was a spectial case of those obtained in Ref. [1]}, [2]}, [3]}. This can be viewed as a direct (A)dS generalization of the Ellis wormhole and the mass is zero.
